Modeling the characteristics of analog distortion devices in reality is more complex: [1]} provides an overview over different methods while discussing DNN-based approaches. In order to simplify the problem for our investigation, we focus on static wave-shaping. The overdrive algorithm of the audio editing software SoX [2]} is an example of static wave-shaping and can be formulated using:
\(\begin{split}d_k &= \lambda _{\mathrm {sc}}(x_{\gamma , k}) - \lambda _{\mathrm {sc}}(x_{\gamma , k-1}) + 0.995 d_{k-1} \\\mathbf {y}_{\mathrm {od}}(\mathbf {x}, \mathbf {d}) &= g_\mathrm {dry} \mathbf {x} + g_\mathrm {wet} \mathbf {d},\end{split}\) 
